Soyuz flights are mostly around 51.8° inclination, and the Soyuz manual gives this as a reference value. Why is 51.8° the standard inclination? That's not the latitude of Baikonur, and I couldn't find any explanation on Google.
As Baikonur is at 45.965° north latitude, it would make sense if 45.965° was the standard inclination for Soyuz (and for the ISS). That would be a launch due east, thereby taking the greatest advantage of the Earth's rotation. The reason the standard inclination is 51.8° is that a failed due east launch might rain debris on China. Avoiding passing over China during launch while still taking as much advantage of the Earth's rotation as possible requires launching a bit north of due east and results in an inclination of at least 51.65° (the inclination of the ISS).